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Averages along polynomial sequences in discrete nilpotent groups: singular Radon transforms
Alexandru D. Ionescu, Akos Magyar, Stephen Wainger
We consider a class of operators defined by taking averages along polynomial sequences in discrete nilpotent groups. In this paper we prove boundedness of discrete singular R…
Singular Radon transforms and maximal functions under convexity assumptions
Andreas Seeger, Stephen Wainger
We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.
Bounds for singular fractional integrals and related Fourier integral operators
Andreas Seeger, Stephen Wainger
We prove sharp L^p-L^q endpoint bounds for singular fractional integral operators and related Fourier integral operators, under the nonvanishing rotational curvature assumption.
Singular and maximal Radon transforms: Analysis and geometry
Michael Christ, Alexander Nagel, Elias M. Stein +1
The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals a…